For clarity and comprehension I would have drawn the PSU like this ...
Code:
CHG + >--------------------.--|>|--.---.---> 12V
CHG - >---. __ | | |
| .--|__|--|<|--' | |
| | 10 | `---> LOAD +
BAT + <>--|--^-----.----------|>|--' .---> LOAD -
BAT - <>--| .|. |
| 47K |_| __|__
| | | |
| }---> >---| FET |
| .|. |_____|
| 10K |_| |
| | |
-^- -^- -^-